2026 NCHS P2 Q6

Triangular plot of land, \(SAC\), is a playground on horizontal ground with a walking path, \(SB\).

\(SC=24\text{ m}\) and \(SB=x\text{ m}\).

The bearing of \(B\) from \(S\) is \(070^\circ\).

The bearing of \(C\) from \(S\) is \(120^\circ\).

The point \(B\) lies on \(AC\) such that \(AB:BC=2:3\).

1. Show that the area of triangle \(SAB\) is \(8x\sin50^\circ\).[4]
2. Hence, find the value of \(x\) given that the area of triangle \(SAB\) is \(110\text{ m}^2\).[1]
3. Find the length of \(BC\).[2]
4. Find the bearing of \(B\) from \(C\).[3]